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Subjects

Mathematics

Complement of a Set and Its Properties

समुच्चय का पूरक और उसके गुणधर्म

In Class 11 Mathematics, under the chapter Sets, Complement of a Set and Its Properties explains the elements of a universal set that are not in a given set. Students find complements using notation such as A′, determine complements from given sets, and understand basic relationships between a set, its complement, and the universal set.

Practice questions

If U = {1, 2, 3, ..., 15} and A is the set of elements of U that are multiples of 5, what is Aᶜ?If U = {a, e, i, o, u, b, c, d} and A = {a, e, i, o, u}, what is Aᶜ?If U = {1, 2, 3, 4, 5, 6, 7, 8}, A = {1, 2, 7}, and B = {2, 3, 8}, what is (A ∪ B)ᶜ?If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8}, and B = {3, 6, 9}, what is (A ∩ B)ᶜ?If the universal set U has n(U) = 72 and n(Aᶜ) = 31, what is the value of n(A)?If the universal set is U = [0, 12] and A = (3, 8], what is the complement Aᶜ of A with respect to U?If U = {x ∈ ℤ | -3 ≤ x ≤ 4} and A = {-2,0,2,4}, what is Aᶜ?In a class, U is the set of all students and A is the set of students who like mathematics. If n(U) = 55 and n(A) = 37, how many students do not like mathematics, that is, n(Aᶜ)?If B is called the complement of A, which statement must be true?Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, A = {2, 4, 6, 8, 10, 12}, and B = {3, 6, 9, 12}. What is Aᶜ ∩ Bᶜ?If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5}, and B = {4,5,6,7}, what is Aᶜ ∪ Bᶜ?If U = {x ∈ ℕ | 1 ≤ x ≤ 20} and A = {x ∈ U | x is a prime number}, how many elements does Aᶜ contain?Let U = {x : x ∈ ℤ, -4 ≤ x ≤ 4} and A = {x : x² ≤ 4}. What is the complement Aᶜ of A with respect to U?If the universal set is U = [-2, 6] and A = (1, 4], what is the complement Aᶜ of A with respect to U?If U = (-5,5] and A = [-1,3), what is Aᶜ?If A ⊆ B ⊆ U, which of the following is always true?If Aᶜ ⊆ Bᶜ, which of the following conclusions is correct?If \(A\subseteq U\), which statement is always true with respect to the universal set \(U\)?If \(n(U)=100\), \(n(A^c)=40\), \(n(B^c)=55\), and \(n(A^c\cap B^c)=20\), what is \(n(A\cap B)\)?If the universal set is \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\), and \(B=\{4,5,6\}\), what is the value of \(A^c-B^c\)?